A Transactions Based Model of the Monetary Transmission Mechanism: Part 1

What are the effects of open market operations? How do these differ from money falling from heaven? We propose a new explanation of how open market operations can change real and nominal interest rates which emphasizes three often mentioned but seldom explicitly articulated features of actual monetary economies: i) going to the bank is costly so that people will tend to bunch cash withdrawals, ii) people don't all go to the bank simultaneously and, because of these, iii) at any instant of time agents hold different amounts of cash. We show that these considerations imply that an open market purchase of a bond for fiat money will drive down nominal and real interest rates, lead to a delayed positive price response, and have damped persistent effects on both prices and nominal interest rates if agents have logarithmic utility of consumption. We assume output is exogenous, so that the model can shed only indirect light on the relationship between money and aggregate output. The model has emphasized how a change in the money supply affects the spending decision of those agents making withdrawals at the time of an open market operation. Considerations of intertemporal substitution imply that the real rate must decline to induce these agents to consume more. Because this new money is spent gradually, prices will rise slowly and reach their steady state level long after the interval of time between trips to the bank.